AIMs: Define, calculate, and interpret confidence intervals for regression coefficients. Define and interpret hypothesis tests about regression coefficients.
Questions:
217.1. We regressed a security's returns, S(i), against market index returns, M(i), in order to estimate the security's beta according to R(i) = intercept + beta*M(i). The sample size is 48. The regression output is: R(i) = 0.020 + 1.080*M(i). The standard error of the intercept, SE(intercept), is 0.030; the standard error of the beta, SE(beta), is 0.050. The two-sided null hypothesis is that the security's beta is one; i.e., the null is beta = 1.0. Do we reject the null at 95% confidence?
a. No, the t-statistic is 1.60
b. No, the t-statistic is 21.60
c. Yes, the t-statistic is 5.85
d. Yes, the t-statistic is 21.60
217.2. Assuming the relationship that Earnings = B(0) + B(1)*YearsEducation, hourly earnings ("Earnings" is the regressand or dependent variable) are regressed against years of education ("YearsEducation" is the regressor or independent variable). The OLS regression estimates are given by: Earnings = $3.80 + 2.10*YearsEducation. The standard errors are, SE[B(0)] = 1.62 and SE[(B1)] = 0.28. What is the 95% confidence interval for the average hourly increase for each additional year of education; i.e., what is the confidence interval for the slope coefficient?
a. 1.38 < B(1) < 2.82
b. 1.44 < B(1) < 2.76
c. 1.55 < B(1) < 2.65
d. 1.64 < B(1) < 2.56
217.3. Let (X) represent a binary variable where either X = 1 if an obligor has a speculative-grade credit rating, or X = 0 if an obligor has an investment-grade credit rating (S&P BBB- or Moody's Baa3 or higher). We assume this regression, R(i) = B(0) + B(1)*X(i), such that returns, R(i), are greater for speculative-grade bonds. The resulting OLS estimate is given by: R(i) = 0.040 + 0.050*X(i). The standard errors are: SE[B(0)] = 0.060 and SE[B(1)] = 0.010. The two-sided null hypothesis is that credit rating has no impact on returns. With 95% confidence, do we reject the null?
a. No, the t-statistic is 0.050
b. No, the t-statistic is 1.050
c. Yes, the t-statistic is 2.0
d. Yes, the t-statistic is 5.0
Answers:
Questions:
217.1. We regressed a security's returns, S(i), against market index returns, M(i), in order to estimate the security's beta according to R(i) = intercept + beta*M(i). The sample size is 48. The regression output is: R(i) = 0.020 + 1.080*M(i). The standard error of the intercept, SE(intercept), is 0.030; the standard error of the beta, SE(beta), is 0.050. The two-sided null hypothesis is that the security's beta is one; i.e., the null is beta = 1.0. Do we reject the null at 95% confidence?
a. No, the t-statistic is 1.60
b. No, the t-statistic is 21.60
c. Yes, the t-statistic is 5.85
d. Yes, the t-statistic is 21.60
217.2. Assuming the relationship that Earnings = B(0) + B(1)*YearsEducation, hourly earnings ("Earnings" is the regressand or dependent variable) are regressed against years of education ("YearsEducation" is the regressor or independent variable). The OLS regression estimates are given by: Earnings = $3.80 + 2.10*YearsEducation. The standard errors are, SE[B(0)] = 1.62 and SE[(B1)] = 0.28. What is the 95% confidence interval for the average hourly increase for each additional year of education; i.e., what is the confidence interval for the slope coefficient?
a. 1.38 < B(1) < 2.82
b. 1.44 < B(1) < 2.76
c. 1.55 < B(1) < 2.65
d. 1.64 < B(1) < 2.56
217.3. Let (X) represent a binary variable where either X = 1 if an obligor has a speculative-grade credit rating, or X = 0 if an obligor has an investment-grade credit rating (S&P BBB- or Moody's Baa3 or higher). We assume this regression, R(i) = B(0) + B(1)*X(i), such that returns, R(i), are greater for speculative-grade bonds. The resulting OLS estimate is given by: R(i) = 0.040 + 0.050*X(i). The standard errors are: SE[B(0)] = 0.060 and SE[B(1)] = 0.010. The two-sided null hypothesis is that credit rating has no impact on returns. With 95% confidence, do we reject the null?
a. No, the t-statistic is 0.050
b. No, the t-statistic is 1.050
c. Yes, the t-statistic is 2.0
d. Yes, the t-statistic is 5.0
Answers:
